Solve for $x$ and $y$ using elimination. ${-3x-5y = -51}$ ${3x+4y = 45}$
Answer: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $-3x$ and $3x$ cancel out. $-y = -6$ $\dfrac{-y}{{-1}} = \dfrac{-6}{{-1}}$ ${y = 6}$ Now that you know ${y = 6}$ , plug it back into $\thinspace {-3x-5y = -51}\thinspace$ to find $x$ ${-3x - 5}{(6)}{= -51}$ $-3x-30 = -51$ $-3x-30{+30} = -51{+30}$ $-3x = -21$ $\dfrac{-3x}{{-3}} = \dfrac{-21}{{-3}}$ ${x = 7}$ You can also plug ${y = 6}$ into $\thinspace {3x+4y = 45}\thinspace$ and get the same answer for $x$ : ${3x + 4}{(6)}{= 45}$ ${x = 7}$